Molar Thermodynamic Functions Research Articles

Calorimetric Studies and Thermodynamic Modeling of Ag-Mg-Ti Liquid Alloys.

Due to the absence of thermodynamic data concerning the Ag-Mg-Ti system in the existing literature, this study aims to fill this gap by offering the outcomes of calorimetric investigations conducted on ternary liquid solutions of these alloys. The measurements were performed using the drop calorimetry method at temperatures of 1294 K and 1297 K for the liquid solutions with the following constant mole fraction ratio: xAg/xMg = 9/1, 7/3, 1/1, 3/7 [(Ag0.9Mg0.1)1-xTix, (Ag0.7Mg0.3)1-xTix, (Ag0.5Mg0.5)1-xTix, (Ag0.3Mg0.7)1-xTix)], and xAg/xTi = 19/1 [(Ag0.95Ti0.05)1-xMgx]. The results show that the mixing enthalpy change is characterized by negative deviations from the ideal solutions and the observed minimal value equals -13.444 kJ/mol for the Ag0.95Ti0.05 alloy and xMg = 0.4182. Next, based on the thermodynamic properties of binary systems described by the Redlich-Kister model and the determined experimental data from the calorimetric measurements, the ternary optimized parameters for the Ag-Mg-Ti liquid phase were calculated by the Muggianu model. Homemade software (TerGexHm 1.0) was used to optimize the calorimetric data using the least squares method. Next, the partial and molar thermodynamic functions were calculated and are presented in the tables and figures. Moreover, this work presents, for comparative purposes, the values of the enthalpy of mixing of liquid Ag-Mg-Ti alloys, which were calculated using Toop's model. It was found that the best agreement between the modeled and experimental data was observed for the cross-sections xAg/xTi = 19/1 [(Ag0.95Ti0.05)1-xMgx] and xAg/xMg = 9/1 [(Ag0.9Mg0.1)1-xTix]. The results of the experiments presented in this paper are the first step in the investigation and future evaluation of the thermodynamics of phases and the calculation of the phase diagram of the silver-magnesium-titanium system.

Molar and partial molar thermodynamic functions of [BMIm]BF4/water mixture (Gibbs free energy, entropy and enthalpy)

ABSTRACT The viscosity of a 1-butyl-3-methylimidazolium tetrafluoroborate ([BMIm]BF4)/water mixture has been reported to be less than one-half that of pure [BMIm]BF4 for water mole fraction (χ w) of 0.3, even though the liquid structure of [BMIm]BF4 has been reported to be similar to that of pure [BMIm]BF4 for 0 ≤ χ w ≤ 0.7. To investigate the relationship between the liquid structure and viscosity, the water content dependence of the viscosity is discussed in terms of the molar and partial molar thermodynamic functions calculated from the density and viscosity of the [BMIm]BF4/water mixture. A schematic model is then proposed based on the results. In the water fraction region of 0–0.3, water molecules enter into the liquid structure of [BMIm]BF4. Water molecules do not interact strongly with [BMIm]BF4 and have much higher mobility than [BMIm]BF4; therefore, it is expected that the water molecules enhance the fluidity of [BMIm]BF4 as a lubricant.

Solubility behavior of CO2 and H2S in 1-benzyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ionic liquid

The solubility of CO2 and H2S in 1-benzyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([Bzmim][Tf2N]) ionic liquid has been measured at temperatures from (303.15 to 343.15) K and pressures of up to about 3.1 and 1.6 MPa, respectively. The molar volume of the gas saturated liquid phase has also been measured. It was found that the solubility of H2S in [Bzmim][Tf2N] is>2 times that of CO2. Henry’s constants, partial molar volumes and partial molar thermodynamic functions at infinite dilution for dissolution of CO2 and H2S in [Bzmim][Tf2N] were evaluated from the experimental data. The experimental data was correlated using the extended Henry's law combined with a simplified Pitzer's model. The experimental data was further correlated by a generic Redlich-Kwong equation of state (GRK EoS). Both models show quite good correlative accuracy for CO2/H2S + [Bzmim][Tf2N] mixtures. However, the former model was superior to that of the GRK EoS for H2S + [Bzmim][Tf2N].

Molar Thermodynamic Functions of the Improved Scarf Ii Oscillator

Molar Thermodynamic Functions of the Improved Scarf Ii Oscillator

Calorimetric studies and thermodynamic properties of Li-Pb-Pd liquid alloys

The first ever calorimetric results of integral enthalpies of mixing of liquid Li-Pb-Pd alloys were investigated with the use of an MHTC 96 drop calorimeter. Five separate measurements were performed for such liquid alloys as (Li0.5Pb0.50)1−xPdx, (Li0.25Pb0.75)1−xPdx at 926 K, (Pb0.90Pd0.10)1−xLix at 1005 K, as well as (Li0.75Pb0.25)1−xPdx, and (Pb0.60Pd0.40)1−xLix at 1026 K. Based on the authors' own equations describing the excess Gibbs energy of binary Li-Pb, Li-Pd, and Pb-Pd liquid solutions, and the experimental values of integral molar enthalpy of mixing of liquid Li-Pb-Pd alloys presented in this work, the ternary interaction parameters were calculated. Finally, the values of molar thermodynamic functions of liquid Li-Pb-Pd alloys were calculated and presented in the form of tables and figures.

Thermodynamic characteristics of liquid metallic alloys containing lead, antimony and bismuth

An improved construction of the electrochemical cell and optimized technique for measuring the electromotive forces (EMF) of liquid metallic Pb-Bi-Sb, Pb-Bi and Pb-Sb alloys in the KCl-PbCl2 melt are described in this paper. Proposed extensions allowed studying alloys of three different compositions simultaneously and increasing the reliability of the experimental EMF values. A simplified procedure for calculating integral molar thermodynamic functions of binary and ternary systems by the Darken method using only standard Excel tools is described in detail. Dependences of the integral excess Gibbs energy and entropy, integral molar Gibbs energy, mixing entropy and mixing enthalpy on the antimony mole fraction are calculated at 973 K for the Bi-Sb system, which cannot be studied by the EMF method due to the proximity of Bi and Sb potentials in the electrochemical series. The results confirm that the developed techniques are promising for determining thermodynamic characteristics of one of the binary systems without experimental study.

Phonon density of states and thermodynamic properties of La2(C11H19O2)6

Based on the low-temperature heat capacity a set of properties of dimeric lanthanum dipivaloylmethanate were obtained. The phonon density of states was calculated, and characteristic temperatures related to the basic moments of the density of states were obtained. The molar thermodynamic functions at constant volume (heat capacity, entropy, internal energy increment, and Helmholtz energy) in the temperature range of 0–455 K were calculated. The molar zero-point energy and total internal energy were calculated.

Phase Equilibria in the Ag2Te-PbTe-Sb2Te3 System and Thermodynamic Properties of the (2PbTe)1-x(AgSbTe2)x Solid Solutions

Phase equilibria in the Ag2Te-PbTe-Sb2Te3 system were experimentally investigated by means of differential thermal analysis, powder X-ray diffraction techniques and electromotive force (EMF) measurement method. A liquidus surface projection of the system, 750 K and 300 K isothermal sections, as well as five vertical sections of the phase diagram, were constructed. The primary crystallization fields of phases and homogeneity range of phases were also determined. The character and temperature of the various nonvariant and monovariant equilibria were identified. The studied sys-tem is characterized by the formation of a wide continuous band of a high-temperature cubic structured solid solution (?-phase) between PbTe and Ag1-xSb1 + xTe2 + x intermediate phase. The partial molar thermodynamic functions of lead telluride in alloys and standard integral thermodynamic functions of the ?-solid solutions along the 2PbTe-AgSbTe2 section were calculated based on the EMF measurements results.

Phonon density of states and thermodynamic properties of Eu2(C11H19O2)6

In the work, the phonon density of states of europium dipivaloylmethanate was calculated based on the experimental low-temperature heat capacity, and basic characteristic temperatures related to the moments of the g(ω) were obtained. The molar thermodynamic functions of Eu2(C11H19O2)6 at constant volume up to the melting point of 464 K were calculated: heat capacity, entropy, internal energy, and Helmholtz energy. The zero-point energy was determined, and total internal energy was obtained. Accuracy of the obtained results was estimated. The approach used to obtain the properties of Eu2(C11H19O2)6 is general, it can be used to study a wide range of solids.

Activity coefficients of lanthanum in gallium and gallium-aluminum based alloys

Activity of β-lanthanum were determined in gallium and gallium-aluminum alloy (12 mol. % Al) at 573–1081 K and 573–999 K, respectively, using the electromotive force measurements method. Partial molar thermodynamic functions of lanthanum in the said alloys were calculated. Solubility of lanthanum in liquid gallium was measured between 368 and 1073 K and activity coefficients of β-lanthanum in liquid Ga and Ga–Al alloy calculated. Comparison of results obtained for La–Ga and La–Ga–Al alloys showed that addition of aluminum to Ga–La alloys had an insignificant influence on thermodynamic properties of lanthanum.

Thermal energy storage and thermodynamic properties of (E)-3-m-tolylbut-2-enoic acid as a medium temperature phase change material

ABSTRACTPhase change materials (PCMs) that can store and release heat energy over the temperature range from 363 to 393 K are crucial for solar absorption cooling, and it is worthy to seek new solid-liquid PCMs candidates that melt and crystallize in this temperature range. In this paper, (E)-3-m-tolylbut-2-enoic acid (mTBEA) was applied as a PCM candidate. Its thermal energy storage properties and thermal stability were systematically investigated. The results showed that mTBEA melted at 382.9 ± 0.5 K and crystallized at about 364 K, with a melting enthalpy (ΔfusH) of 138.4 ± 6.9 J g−1 and showed good long-term cyclic stability and thermal stability. The supercooling of mTBEA was stabilized at about 20 K, indicating that the conservation condition of melted mTBEA could be simple. In addition, the melted mTBEA could release all the absorbed thermal energy upon crystallizing. Besides, mTBEA exhibited good thermal stability for it to be applied as PCM. Hence, mTBEA is a promising PCM candidate for solar absorption cooling. Furthermore, the heat capacity of mTBEA was measured by modulated temperature differential scanning calorimetry (MTDSC) over the temperature range from 198.15 to 431.15 K, and the molar thermodynamic functions, [HT-H298.15]m and [ST-S298.15]m, were calculated based on the fitted molar heat capacity data.

Thermodynamic characteristics of praseodymium in the gallium–aluminum eutectic melt

The Ga–Al eutectic melt saturated with praseodymium was studied in the temperature range 572–1076 K by electromotive force (emf) method relative to the reference electrode (InL + PrIn3, where L is the liquid phase) in a LiCl–KCl–CsCl eutectic electrolyte. The partial molar thermodynamic functions (enthalpy, entropy, and Gibbs energy) of praseo dymium in a Ga–Al eutectic melt were calculated. According to the emf measurements of the two-phase Pr–Ga–AlL + intermetallic compound alloys equilibrated with the Ga–Al eutectic melt saturated with praseodymium, there are intermetallic compounds PrGa6, PrGa4, and Pr0.22Ga0.78(PrGa2) in the temperature ranges 572–741, 741–883, and 883–1076 K, respectively.

Thermodynamic properties of 2–methylindole: Experimental and computational results for gas-phase entropy and enthalpy of formation

Abstract Measurements leading to the calculation of thermodynamic properties in the ideal-gas state for 2-methylindole (Chemical Abstracts registry number [95–20–5]) are reported. Experimental methods were adiabatic heat-capacity calorimetry, differential scanning calorimetry (d.s.c.), comparative ebulliometry, inclined-piston manometry, and oxygen bomb calorimetry. The critical temperature of 2-methylindole was determined experimentally with d.s.c. Molar thermodynamic functions for the condensed and ideal-gas states were derived from the experimental results. Statistical calculations were performed based on molecular geometry optimization and vibrational frequencies using B3LYP hybrid density functional theory with the def2-TZVPPD basis set. Excellent accord between computed and experimentally-derived ideal-gas entropies is shown. The enthalpy of formation for 2-methylindole in the gas phase was computed with an atomization-based protocol described recently, and excellent agreement with the experimental values is seen. The experimental literature for enthalpies of formation in the gas phase for 1- and 2-ring pyrrollic compounds is reviewed, and comparisons with computed values further support the findings here. All experimental results are compared with property values reported in the literature, where possible.

Thermodynamic description of the Ge-In-Li liquid alloys

The integral molar mixing enthalpy of liquid ternary Ge-In-Li alloys was investigated using drop calorimetry method. Five separate measurements of (In0.75Li0.25)1-xGex, (In0.50Li0.50)1-xGex, and (In0.25Li0.75)1-xGex, (Ge0.50Li0.50)1-xInx and (Ge0.50In0.50)1-xLix liquid alloys at 1076K were studied. Next, the ternary interaction parameters were calculated based on available in literature equations describing the excess Gibbs energy of binary Ge-Li, Ge-In and In-Li liquid solutions (the Redlich-Kister relation), and presented in this work experimental values of mixing enthalpy of liquid Ge-In-Li alloys. Finally, the values of partial and molar thermodynamic functions of liquid ternary Ge-In-Li alloys for the fixed temperature of 1076K and for the constant rations of In/Li, Ge/Li and Ge/In as mentioned above were calculated and presented in the form of tables and figures.

Oxygen nonstoichiometry and thermodynamic quantities in solid solution SrFe1–xSnxO3–δ

The oxygen content (3–δ) variations in tin substituted derivatives SrFe1–xSnxO3–δ, where x = 0.05, 0.1, 0.17 and 0.25, of perovskite-like strontium ferrite, have been studied by coulometric titration measurements within oxygen partial pressure (pO2) range 10–19–10–2 atm at 800–950 °С. The obtained dependencies of (3–δ) from pO2 and temperature are used for calculations of partial molar thermodynamic functions of oxygen in the oxide structure. It is found that a satisfactory explanation of the experimental results can be attained within frameworks of the ideal solution model with ion and electron defects appearing in the result of oxidation and disproportionation of iron cations. The increase of the oxidation reaction enthalpy with tin content is consistent with the increase of the unit cell parameter, i.e., the stretch and relaxation of Fe-O chemical bonds.

Excess thermodynamic functions in aqueous systems containing soluble fullerene derivatives

Using a Beckman thermometer, the concentration dependence of water crystallization temperatures was investigated for C60(OH)22–24 – H2O, C70(OH)12 – H2O, C70[C(COOH)2]3 – H2O, С60(C5H9NO3)2 - H2O, С60(C6H14N2O2)2 – H2O binary systems. The semi-empirical Virial Decomposition Asymmetric Model of virial expansion of the excess Gibbs energy of the light fullerene derivatives solutions was applied. On the basis of the proposed model, partial and average molar thermodynamic functions of binary solutions as well as the conditions of stability against phase separation were determined.

ТЕРМОДИНАМИЧЕСКИЕ СВОЙСТВА ТВЕРДЫХ РАСТВОРОВ В СИСТЕМЕ Cu8GeS6 - Ag8GeS6

Измерением ЭДС концентрационных цепей с твердым электролитом Cu4RbCl3I2 в интервале температур 300÷380 К изучена система Cu8GeS6-Ag8GeS6. Показано образование широких областей твердых растворов на основе исходных соединений. Из данных измерений ЭДС вычислены парциальные молярные функции меди в сплавах.

Thermodynamic properties of pyrrole, 1-methylpyrrole, 2,4-dimethylpyrrole, and 2,5-dimethylpyrrole: Experimental and computational results

New measurements of critical temperature, saturated liquid heat capacity from temperature T≈315K to T≈550K, and saturated liquid density from T=323K to T≈475K are reported for pyrrole (Chemical Abstracts registry number [109-97-7]), 1-methylpyrrole [96-54-8], 2,4-dimethylpyrrole [625-82-1], and 2,5-dimethylpyrrole [625-84-3]. New measurements of vapor pressure are reported for 2,4-dimethylpyrrole {338<(T/K)<477} and 2,5-dimethylpyrrole {341<(T/K)<479}, as well as the enthalpy of combustion determined with oxygen-bomb calorimetry for 2,4-dimethylpyrrole. These new measurements are combined with literature values to calculate thermodynamic properties in the ideal-gas state for extended ranges of temperature for all compounds: pyrrole {298<(T/K)<550}, 1-methylpyrrole {298<(T/K)<530}, 2,4-dimethylpyrrole {298<(T/K)<600}, and 2,5-dimethylpyrrole {298<(T/K)<560}. Molar thermodynamic functions (enthalpies, entropies, and Gibbs energies) for the liquid and ideal-gas states were derived from the experimental studies at selected temperatures. Statistical calculations were performed with optimized geometries, scaled vibrational frequencies, and methyl rotational potentials performed using B3LYP hybrid density functional theory with the def2-TZVPPD basis set. Methyl torsional barriers were evaluated at the DLPNO-CCSD(T)/def2-QZVP level of theory using the B3LYP/def2-TZVPPD geometries. Computed ideal-gas properties are shown to be in excellent accord with ideal-gas entropies derived from thermophysical property measurements, as well as with reported experimental heat capacities for the ideal-gas state. All experimental results are compared with property values available in the literature.

Molar heat capacities and thermodynamic functions for difluoromethyleneoxy-bridged liquid crystalline compounds

Differential scanning calorimetry measurements performed in the temperature range of 253–393 K for CF2O linkage liquid crystals reveal existence and stability of the phase transitions. Then, we report molar heat capacities for three difluoromethyleneoxy liquid crystalline compounds measured by the heat-pulse relaxation method within the temperature range from 1.9 to 300 K. The heat capacities of these three compounds increase with the temperature increasing and no thermal anomalies have been found in the whole temperature region. The experimental data have been fitted to a function of temperature with a series of theoretical and empirical models for the proper temperature ranges. Standard thermodynamic properties of these three fluorinated liquid crystals are evaluated from the experimental heat capacity temperature dependencies. The standard molar heat capacities of 3-CB(F,F)XB(F,F)-F, 2-BB(F,F)XB(F,F)-F and 2-BB(F)B(F,F)XB(F,F)-F at 298.15 K and 0.1 MPa have been determined to be $$ C_{{{\text{p}},{\text{m}}}}^{\text{o}} $$ = (560.84 ± 5.61) and (464.41 ± 4.64) and (560.58 ± 5.61) J K−1 mol−1, respectively.

Phase Equilibria in the Ag2Te-SnTe-Sb2Te3 System and Thermodynamic Properties of the (2SnTe)1−x (AgSbTe2) x Solid Solution

Phase equilibria in the Ag2Te-SnTe-Sb2Te3 system were experimentally investigated by means of differential thermal analysis, powder x-ray diffraction techniques, microhardness and electromotive force measurements (EMF) of concentration chains with Ag4RbI5 solid electrolyte. A liquidus surface projection of the system, 700 and 400 K isothermal sections, as well as four vertical sections of the phase diagram were constructed. The primary crystallization fields of phases and homogeneity range of phases were also determined. The character and temperature of the various non- and monovariant equilibria were identified. The system includes a high-temperature cubic structured solid solution along the SnTe-“AgSbTe2” section, which partially (0-15 mol.% SnTe) decompose below 630 K. The partial molar thermodynamic functions of silver in alloys and standard integral thermodynamic functions of the (2SnTe)1−x (AgSbTe2) x (where x = 0.1; 0.2; 0.4; 0.6 and 0.8) solid solution were calculated based on the EMF measurements results.